The inflationary expansion also solves the horizon problem. The basic
strategy is to ensure that

(32)

so that light can travel much further before decoupling than it can
afterwards. This cannot be done with standard evolution, but can be achieved
by inflation.

An alternative way to view this is to remember that inflation
corresponds to a decreasing comoving Hubble length. The Hubble length
is ordinarily a good measure of how far things can travel in the
Universe; what this is telling us is that the region of the Universe we
can see after (even long after) inflation is much smaller than the
region which would have been visible before inflation started. Hence
causal physics was perfectly capable of producing a large smooth
thermalized region, encompassing a volume greatly in excess of our
presently observable Universe. In Figure 2, the outer
circle indicates the initial Hubble length, encompassing the shaded
smooth patch. Inflation shrinks this dramatically inwards towards the
dot indicating our position, and then after inflation it increases
while staying within the initial smooth patch.
(3)

Figure 2. Solving the horizon problem. Initially
the
Hubble length is large, and a smooth patch forms by causal interactions.
Inflation then shrinks the Hubble length, and even the subsequent expansion
again after inflation leaves the observable Universe within the smoothed
patch.

Equally, causal processes would be capable of generating irregularities
in the Universe on scales greatly exceeding our presently observable
Universe, provided they happened at an early enough time that those
scales were within causal contact. This will be explored in detail
later.

3 Although this
is a standard description, it isn't totally accurate. A more accurate
argument is as follows.
[2] At the
beginning of inflation
particles are distributed in a set of modes. This may be a thermal
distribution or something else; whatever, since the energy density is
finite there will be a shortest wavelength occupied mode, e.g. for a
thermal distribution
max ~
1/T. Expressed in
physical coordinates, once inflation has stretched all modes including
this one to be much larger than the Hubble length, the Universe becomes
homogeneous. In comoving coordinates, the equivalent picture is that
the Hubble length shrinks in until it's much smaller than the shortest
wavelength, and the Universe, as before, appears homogeneous.
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